A tewescope's wight gadering power and abiwity to resowve smaww detaiw is directwy rewated to de diameter (or aperture) of its objective (de primary wens or mirror dat cowwects and focuses de wight). The warger de objective, de more wight de tewescope cowwects and de finer detaiw it resowves.

The tewescope is more a discovery of opticaw craftsmen dan an invention of a scientist.[1][2] The wens and de properties of refracting and refwecting wight had been known since antiqwity and deory on how dey worked were devewoped by ancient Greek phiwosophers, preserved and expanded on in de medievaw Iswamic worwd, and had reached a significantwy advanced state by de time of de tewescope's invention in earwy modern Europe.[3][4] But de most significant step cited in de invention of de tewescope was de devewopment of wens manufacture for spectacwes,[2][5][6] first in Venice and Fworence in de dirteenf century,[7] and water in de spectacwe making centers in bof de Nederwands and Germany.[8] It is in de Nederwands in 1608 where de first recorded opticaw tewescopes (refracting tewescopes) appeared. The invention is credited to de spectacwe makers Hans Lippershey and Zacharias Janssen in Middewburg, and de instrument-maker and optician Jacob Metius of Awkmaar.[9]

The next big step in de devewopment of refractors was de advent of de Achromatic wens in de earwy 18f century,[11] which corrected de chromatic aberration in Kepwerian tewescopes up to dat time—awwowing for much shorter instruments wif much warger objectives.

For refwecting tewescopes, which use a curved mirror in pwace of de objective wens, deory preceded practice. The deoreticaw basis for curved mirrors behaving simiwar to wenses was probabwy estabwished by Awhazen, whose deories had been widewy disseminated in Latin transwations of his work.[12] Soon after de invention of de refracting tewescope Gawiweo, Giovanni Francesco Sagredo, and oders, spurred on by deir knowwedge dat curved mirrors had simiwar properties as wenses, discussed de idea of buiwding a tewescope using a mirror as de image forming objective.[13] The potentiaw advantages of using parabowic mirrors (primariwy a reduction of sphericaw aberration wif ewimination of chromatic aberration) wed to severaw proposed designs for refwecting tewescopes,[14] de most notabwe of which was pubwished in 1663 by James Gregory and came to be cawwed de Gregorian tewescope,[15][16] but no working modews were buiwt. Isaac Newton has been generawwy credited wif constructing de first practicaw refwecting tewescopes, de Newtonian tewescope, in 1668[17] awdough due to deir difficuwty of construction and de poor performance of de specuwum metaw mirrors used it took over 100 years for refwectors to become popuwar. Many of de advances in refwecting tewescopes incwuded de perfection of parabowic mirror fabrication in de 18f century,[18] siwver coated gwass mirrors in de 19f century, wong-wasting awuminum coatings in de 20f century,[19]segmented mirrors to awwow warger diameters, and active optics to compensate for gravitationaw deformation, uh-hah-hah-hah. A mid-20f century innovation was catadioptric tewescopes such as de Schmidt camera, which uses bof a wens (corrector pwate) and mirror as primary opticaw ewements, mainwy used for wide fiewd imaging widout sphericaw aberration, uh-hah-hah-hah.

Schematic of a Kepwerianrefracting tewescope. The arrow at (4) is a (notionaw) representation of de originaw image; de arrow at (5) is de inverted image at de focaw pwane; de arrow at (6) is de virtuaw image dat forms in de viewer's visuaw sphere. The red rays produce de midpoint of de arrow; two oder sets of rays (each bwack) produce its head and taiw.

Most tewescope designs produce an inverted image at de focaw pwane; dese are referred to as inverting tewescopes. In fact, de image is bof turned upside down and reversed weft to right, so dat awtogeder it is rotated by 180 degrees from de object orientation, uh-hah-hah-hah. In astronomicaw tewescopes de rotated view is normawwy not corrected, since it does not affect how de tewescope is used. However, a mirror diagonaw is often used to pwace de eyepiece in a more convenient viewing wocation, and in dat case de image is erect, but stiww reversed weft to right. In terrestriaw tewescopes such as spotting scopes, monocuwars and binocuwars, prisms (e.g., Porro prisms) or a reway wens between objective and eyepiece are used to correct de image orientation, uh-hah-hah-hah. There are tewescope designs dat do not present an inverted image such as de Gawiwean refractor and de Gregorian refwector. These are referred to as erecting tewescopes.

Many types of tewescope fowd or divert de opticaw paf wif secondary or tertiary mirrors. These may be integraw part of de opticaw design (Newtonian tewescope, Cassegrain refwector or simiwar types), or may simpwy be used to pwace de eyepiece or detector at a more convenient position, uh-hah-hah-hah. Tewescope designs may awso use speciawwy designed additionaw wenses or mirrors to improve image qwawity over a warger fiewd of view.

Design specifications rewate to de characteristics of de tewescope and how it performs opticawwy. Severaw properties of de specifications may change wif de eqwipment or accessories used wif de tewescope; such as Barwow wenses, star diagonaws and eyepieces. These interchangeabwe accessories don't awter de specifications of de tewescope, however dey awter de way de tewescopes properties function, typicawwy magnification, apparent fiewd of view and FOV.

The smawwest resowvabwe surface area of an object, as seen drough an opticaw tewescope, is de wimited physicaw area dat can be resowved. It is anawogous to anguwar resowution, but differs in definition: instead of separation abiwity between point-wight sources it refers to de physicaw area dat can be resowved. A famiwiar way to express de characteristic is de resowvabwe abiwity of features such as Moon craters or Sun spots. Expression using de formuwa is given by de sum of twice de resowving power R{\dispwaystywe R} over aperture diameter D{\dispwaystywe D} muwtipwied by de objects diameter Dob{\dispwaystywe D_{ob}} muwtipwied by de constant Φ{\dispwaystywe \Phi } aww divided by de objects apparent diameterDa{\dispwaystywe D_{a}}.[20][21]

Resowving power R{\dispwaystywe R} is derived from de wavewengfλ{\dispwaystywe {\wambda }} using de same unit as aperture; where 550 nm to mm is given by: R=λ106=550106=0.00055{\dispwaystywe R={\frac {\wambda }{10^{6}}}={\frac {550}{10^{6}}}=0.00055}.The constant Φ{\dispwaystywe \Phi } is derived from radians to de same unit as de objects apparent diameter; where de Moonsapparent diameter of Da=313Π10800{\dispwaystywe D_{a}={\frac {313\Pi }{10800}}}radians to arcsecs is given by: Da=313Π10800∗206265=1878{\dispwaystywe D_{a}={\frac {313\Pi }{10800}}*206265=1878}.

An exampwe using a tewescope wif an aperture of 130 mm observing de Moon in a 550 nmwavewengf, is given by: F=2RD∗Dob∗ΦDa=2∗0.00055130∗3474.2∗2062651878≈3.22{\dispwaystywe F={\frac {{\frac {2R}{D}}*D_{ob}*\Phi }{D_{a}}}={\frac {{\frac {2*0.00055}{130}}*3474.2*206265}{1878}}\approx 3.22}

The unit used in de object diameter resuwts in de smawwest resowvabwe features at dat unit. In de above exampwe dey are approximated in kiwometers resuwting in de smawwest resowvabwe Moon craters being 3.22 km in diameter. The Hubbwe Space Tewescope has a primary mirror aperture of 2400 mm dat provides a surface resowvabiwity of Moon craters being 174.9 meters in diameter, or sunspots of 7365.2 km in diameter.

Here, αR{\dispwaystywe \awpha _{R}} denotes de resowution wimit in arcseconds and D{\dispwaystywe D} is in miwwimeters.
In de ideaw case, de two components of a doubwe star system can be discerned even if separated by swightwy wess dan αR{\dispwaystywe \awpha _{R}}. This is taken into account by de Dawes wimit

αD=116D{\dispwaystywe \awpha _{D}={\frac {116}{D}}}

The eqwation shows dat, aww ewse being eqwaw, de warger de aperture, de better de anguwar resowution, uh-hah-hah-hah. The resowution is not given by de maximum magnification (or "power") of a tewescope. Tewescopes marketed by giving high vawues of de maximum power often dewiver poor images.

For warge ground-based tewescopes, de resowution is wimited by atmospheric seeing. This wimit can be overcome by pwacing de tewescopes above de atmosphere, e.g., on de summits of high mountains, on bawwoon and high-fwying airpwanes, or in space. Resowution wimits can awso be overcome by adaptive optics, speckwe imaging or wucky imaging for ground-based tewescopes.

Recentwy, it has become practicaw to perform aperture syndesis wif arrays of opticaw tewescopes. Very high resowution images can be obtained wif groups of widewy spaced smawwer tewescopes, winked togeder by carefuwwy controwwed opticaw pads, but dese interferometers can onwy be used for imaging bright objects such as stars or measuring de bright cores of active gawaxies.

The focaw wengf of an opticaw system is a measure of how strongwy de system converges or diverges wight. For an opticaw system in air, it is de distance over which initiawwy cowwimated rays are brought to a focus. A system wif a shorter focaw wengf has greater opticaw power dan one wif a wong focaw wengf; dat is, it bends de rays more strongwy, bringing dem to a focus in a shorter distance. In astronomy, de f-number is commonwy referred to as de focaw ratio notated as N{\dispwaystywe N}. The focaw ratio of a tewescope is defined as de focaw wengff{\dispwaystywe f} of an objective divided by its diameter D{\dispwaystywe D} or by de diameter of an aperture stop in de system. The focaw wengf controws de fiewd of view of de instrument and de scawe of de image dat is presented at de focaw pwane to an eyepiece, fiwm pwate, or CCD.

An exampwe of a tewescope wif a focaw wengf of 1200 mm and aperture diameter of 254 mm is given by:
N=fD=1200254≈4.7{\dispwaystywe N={\frac {f}{D}}={\frac {1200}{254}}\approx 4.7}

Numericawwy warge Focaw ratios are said to be wong or swow. Smaww numbers are short or fast. There are no sharp wines for determining when to use dese terms, and an individuaw may consider deir own standards of determination, uh-hah-hah-hah. Among contemporary astronomicaw tewescopes, any tewescope wif a focaw ratio swower (bigger number) dan f/12 is generawwy considered swow, and any tewescope wif a focaw ratio faster (smawwer number) dan f/6, is considered fast. Faster systems often have more opticaw aberrations away from de center of de fiewd of view and are generawwy more demanding of eyepiece designs dan swower ones. A fast system is often desired for practicaw purposes in astrophotography wif de purpose of gadering more photons in a given time period dan a swower system, awwowing time wapsed photography to process de resuwt faster.

The wight-gadering power of an opticaw tewescope, awso referred to as wight grasp or aperture gain, is de abiwity of a tewescope to cowwect a wot more wight dan de human eye. Its wight-gadering power is probabwy its most important feature. The tewescope acts as a wight bucket, cowwecting aww of de photons dat come down on it from a far away object, where a warger bucket catches more photons resuwting in more received wight in a given time period, effectivewy brightening de image. This is why de pupiws of your eyes enwarge at night so dat more wight reaches de retinas. The gadering power P{\dispwaystywe P} compared against a human eye is de sqwared resuwt of de division of de apertureD{\dispwaystywe D} over de observer's pupiw diameter Dp{\dispwaystywe D_{p}},[20][21] wif an average aduwt having a pupiw diameter of 7mm. Younger persons host warger diameters, typicawwy said to be 9mm, as de diameter of de pupiw decreases wif age.

An exampwe gadering power of an aperture wif 254 mm compared to an aduwt pupiw diameter being 7 mm is given by: P=(DDp)2=(2547)2≈1316.7{\dispwaystywe P=\weft({\frac {D}{D_{p}}}\right)^{2}=\weft({\frac {254}{7}}\right)^{2}\approx 1316.7}

Light-gadering power can be compared between tewescopes by comparing de areasA{\dispwaystywe A} of de two different apertures.

As an exampwe, de wight-gadering power of a 10 metertewescope is 25x dat of a 2 metertewescope: p=A1A2=π52π12=25{\dispwaystywe p={\frac {A_{1}}{A_{2}}}={\frac {\pi 5^{2}}{\pi 1^{2}}}=25}

The magnification drough a tewescope magnifies a viewing object whiwe wimiting de FOV. Magnification is often misweading as de opticaw power of de tewescope, its characteristic is de most misunderstood term used to describe de observabwe worwd. At higher magnifications de image qwawity significantwy reduces, usage of a Barwow wens—which increases de effective focaw wengf of an opticaw system—muwtipwies image qwawity reduction, uh-hah-hah-hah.

Simiwar minor effects may be present when using star diagonaws, as wight travews drough a muwtitude of wenses dat increase or decrease effective focaw wengf. The qwawity of de image generawwy depends on de qwawity of de optics (wenses) and viewing conditions—not on magnification, uh-hah-hah-hah.

Magnification itsewf is wimited by opticaw characteristics. Wif any tewescope or microscope, beyond a practicaw maximum magnification, de image wooks bigger but shows no more detaiw. It occurs when de finest detaiw de instrument can resowve is magnified to match de finest detaiw de eye can see. Magnification beyond dis maximum is sometimes cawwed empty magnification.

To get de most detaiw out of a tewescope, it is criticaw to choose de right magnification for de object being observed. Some objects appear best at wow power, some at high power, and many at a moderate magnification, uh-hah-hah-hah. There are two vawues for magnification, a minimum and maximum. A wider fiewd of vieweyepiece may be used to keep de same eyepiece focaw wengf whiwst providing de same magnification drough de tewescope. For a good qwawity tewescope operating in good atmospheric conditions, de maximum usabwe magnification is wimited by diffraction, uh-hah-hah-hah.

The visuaw magnification M{\dispwaystywe M} of de fiewd of view drough a tewescope can be determined by de tewescopes focaw wengff{\dispwaystywe f} divided by de eyepiecefocaw wengffe{\dispwaystywe f_{e}} (or diameter).[20][21] The maximum is wimited by de focaw wengf of de eyepiece.

There is a wowest usabwe magnification on a tewescope. The increase in brightness wif reduced magnification has a wimit rewated to someding cawwed de exit pupiw. The exit pupiw is de cywinder of wight coming out of de eyepiece, hence de wower de magnification, de warger de exit pupiw. The minimum Mm{\dispwaystywe M_{m}} can be cawcuwated by dividing de tewescopeapertureD{\dispwaystywe D} over de exit pupiw diameter Dep{\dispwaystywe D_{ep}}.[22] Decreasing de magnification past dis wimit cannot increase brightness, at dis wimit dere is no benefit for decreased magnification, uh-hah-hah-hah. Likewise cawcuwating de exit pupiwDep{\dispwaystywe D_{ep}} is a division of de aperture diameter D{\dispwaystywe D} and de visuaw magnification M{\dispwaystywe M} used. The minimum often may not be reachabwe wif some tewescopes, a tewescope wif a very wong focaw wengf may reqwire a wonger-focaw-wengf eyepiece dan is possibwe.

An exampwe of de wowest usabwe magnification using a 254 mmaperture and 7 mmexit pupiw is given by: Mm=DDep=2547≈36{\dispwaystywe M_{m}={\frac {D}{D_{ep}}}={\frac {254}{7}}\approx 36}, whiwst de exit pupiw diameter using a 254 mmaperture and 36x magnification is given by: Dep=DM=25436≈7{\dispwaystywe D_{ep}={\frac {D}{M}}={\frac {254}{36}}\approx 7}

Fiewd of view is de extent of de observabwe worwd seen at any given moment, drough an instrument (e.g., tewescope or binocuwars), or by naked eye. There are various expressions of fiewd of view, being a specification of an eyepiece or a characteristic determined from and eyepiece and tewescope combination, uh-hah-hah-hah. A physicaw wimit derives from de combination where de FOV cannot be viewed warger dan a defined maximum, due to diffraction of de optics.

Apparent FOV is de observabwe worwd observed drough an ocuwar eyepiece widout insertion into a tewescope. It is wimited by de barrew size used in a tewescope, generawwy wif modern tewescopes dat being eider 1.25 or 2 inches in diameter. A wider FOV may be used to achieve a more vast observabwe worwd given de same magnification compared wif a smawwer FOV widout compromise to magnification, uh-hah-hah-hah. Note dat increasing de FOV wowers surface brightness of an observed object, as de gadered wight is spread over more area, in rewative terms increasing de observing area proportionawwy wowers surface brightness dimming de observed object. Wide FOVeyepieces work best at wow magnifications wif warge apertures, where de rewative size of an object is viewed at higher comparative standards wif minimaw magnification giving an overaww brighter image to begin wif.

True FOV is de observabwe worwd observed dough an ocuwar eyepiece inserted into a tewescope. Knowing de true FOV of eyepieces is very usefuw since it can be used to compare what is seen drough de eyepiece to printed or computerized star charts dat hewp identify what is observed. True FOVvt{\dispwaystywe v_{t}} is de division of apparent FOVva{\dispwaystywe v_{a}} over magnificationM{\dispwaystywe M}.[20][21]

An exampwe of true FOV using an eyepiece wif 52° apparent FOV used at 81.25x magnification is given by: vt=vaM=5281.25=0.64∘{\dispwaystywe v_{t}={\frac {v_{a}}{M}}={\frac {52}{81.25}}=0.64^{\circ }}

Max FOV is a term used to describe de maximum usefuw true FOV wimited by de optics of de tewescope, it is a physicaw wimitation where increases beyond de maximum remain at maximum. Max FOVvm{\dispwaystywe v_{m}} is de barrew size B{\dispwaystywe B} over de tewescopesfocaw wengff{\dispwaystywe f} converted from radian to degrees.[20][21]

There are many properties of opticaw tewescopes and de compwexity of observation using one can be a daunting task; experience and experimentation are de major contributors to understanding how to maximize one's observations. In practice, onwy two main properties of a tewescope determine how observation differs: de focaw wengf and aperture. These rewate as to how de opticaw system views an object or range and how much wight is gadered drough an ocuwar eyepiece. Eyepieces furder determine how de fiewd of view and magnification of de observabwe worwd change.

Observabwe worwd describes what can be seen using a tewescope, when viewing an object or range de observer may use many different techniqwes. Understanding what can be viewed and how to view it depends on de fiewd of view. Viewing an object at a size dat fits entirewy in de fiewd of view is measured using de two tewescope properties—focaw wengf and aperture, wif de incwusion of an ocuwar eyepiece wif suitabwe focaw wengf (or diameter). Comparing de observabwe worwd and de anguwar diameter of an object shows how much of de object we see. However, de rewationship wif de opticaw system may not resuwt in high surface brightness. Cewestiaw objects are often dim because of deir vast distance, and detaiw may be wimited by diffraction or unsuitabwe opticaw properties.

Finding what can be seen drough de opticaw system begins wif de eyepiece providing de fiewd of view and magnification; de magnification is given by de division of de tewescope and eyepiece focaw wengds. Using an exampwe of an amateur tewescope such as a Newtonian tewescope wif an apertureD{\dispwaystywe D} of 130 mm (5") and focaw wengf f{\dispwaystywe f} of 650 mm (25.5 inches), one uses an eyepiece wif a focaw wengf d{\dispwaystywe d} of 8 mm and apparent fiewd of viewva{\dispwaystywe v_{a}} of 52°. The magnification at which de observabwe worwd is viewed is given by: M=fd=6508=81.25{\dispwaystywe M={\frac {f}{d}}={\frac {650}{8}}=81.25}. The true fiewd of viewvt{\dispwaystywe v_{t}} reqwires de magnification, which is formuwated by its division over de apparent fiewd of view: vt=vaM=5281.25=0.64{\dispwaystywe v_{t}={\frac {v_{a}}{M}}={\frac {52}{81.25}}=0.64}. The resuwting true fiewd of view is 0.64°, awwowing an object such as de Orion nebuwa, which appears ewwipticaw wif an anguwar diameter of 65 × 60 arcminutes, to be viewabwe drough de tewescope in its entirety, where de whowe of de nebuwa is widin de observabwe worwd. Using medods such as dis can greatwy increase one's viewing potentiaw ensuring de observabwe worwd can contain de entire object, or wheder to increase or decrease magnification viewing de object in a different aspect.

The surface brightness at such a magnification significantwy reduces, resuwting in a far dimmer appearance. A dimmer appearance resuwts in wess visuaw detaiw of de object. Detaiws such as matter, rings, spiraw arms, and gases may be compwetewy hidden from de observer, giving a far wess compwete view of de object or range. Physics dictates dat at de deoreticaw minimum magnification of de tewescope, de surface brightness is at 100%. Practicawwy, however, various factors prevent 100% brightness; dese incwude tewescope wimitations (focaw wengf, eyepiece focaw wengf, etc.) and de age of de observer.

Age pways a rowe in brightness, as a contributing factor is de observer's pupiw. Wif age de pupiw naturawwy shrinks in diameter; generawwy accepted a young aduwt may have a 7 mm diameter pupiw, an owder aduwt as wittwe as 5 mm, and a younger person warger at 9 mm. The minimum magnificationm{\dispwaystywe m} can be expressed as de division of de apertureD{\dispwaystywe D} and pupiwp{\dispwaystywe p} diameter given by: m=Dd=1307≈18.6{\dispwaystywe m={\frac {D}{d}}={\frac {130}{7}}\approx 18.6}. A probwematic instance may be apparent, achieving a deoreticaw surface brightness of 100%, as de reqwired effective focaw wengf of de opticaw system may reqwire an eyepiece wif too warge a diameter.

Some tewescopes cannot achieve de deoreticaw surface brightness of 100%, whiwe some tewescopes can achieve it using a very smaww-diameter eyepiece. To find what eyepiece is reqwired to get minimum magnification one can rearrange de magnification formuwa, where it is now de division of de tewescope's focaw wengf over de minimum magnification: Fm=65018.6≈35{\dispwaystywe {\frac {F}{m}}={\frac {650}{18.6}}\approx 35}. An eyepiece of 35 mm is a non-standard size and wouwd not be purchasabwe; in dis scenario
to achieve 100% one wouwd reqwire a standard manufactured eyepiece size of 40 mm. As de eyepiece has a warger focaw wengf dan de minimum magnification, an abundance of wasted wight is not received drough de eyes.

The increase in surface brightness as one reduces magnification is wimited; dat wimitation is what is described as de exit pupiw: a cywinder of wight dat projects out de eyepiece to de observer. An exit pupiw must match or be smawwer in diameter dan one's pupiw to receive de fuww amount of projected wight; a warger exit pupiw resuwts in de wasted wight. The exit pupiw e{\dispwaystywe e} can be derived wif from division of de tewescope apertureD{\dispwaystywe D} and de minimum magnificationm{\dispwaystywe m}, derived by: e=Dm=13018.6≈7{\dispwaystywe e={\frac {D}{m}}={\frac {130}{18.6}}\approx 7}. The pupiw and exit pupiw are awmost identicaw in diameter, giving no wasted observabwe wight wif de opticaw system. A 7 mm pupiw fawws swightwy short of 100% brightness, where de surface brightnessB{\dispwaystywe B} can be measured from de product of de constant 2, by de sqware of de pupiw p{\dispwaystywe p} resuwting in: B=2∗p2=2∗72=98{\dispwaystywe B=2*p^{2}=2*7^{2}=98}. The wimitation here is de pupiw diameter; it's an unfortunate resuwt and degrades wif age. Some observabwe wight woss is expected and decreasing de magnification cannot increase surface brightness once de system has reached its minimum usabwe magnification, hence why de term is referred to as usabwe.

These eyes represent a scawed figure of de human eye where 15 px = 1 mm, dey have a pupiw diameter of 7 mm. Figure A has an exit pupiw diameter of 14 mm, which for astronomy purposes resuwts in a 75% woss of wight. Figure B has an exit pupiw of 6.4 mm, which awwows de fuww 100% of observabwe wight to be perceived by de observer.

When using a CCD to record observations, de CCD is pwaced in de focaw pwane. Image scawe (sometimes cawwed pwate scawe) describes how de anguwar size of de object being observed is rewated to de physicaw size of de projected image in de focaw pwane

i=αs,{\dispwaystywe i={\frac {\awpha }{s}},}

where i{\dispwaystywe i} is de image scawe, α{\dispwaystywe \awpha } is de anguwar size of de observed object, and s{\dispwaystywe s} is de physicaw size of de projected image. In terms of focaw wengf image scawe is

i=1f,{\dispwaystywe i={\frac {1}{f}},}

where i{\dispwaystywe i} is measured in radians per meter (rad/m), and f{\dispwaystywe f} is measured in meters. Normawwy i{\dispwaystywe i} is given in units of arcseconds per miwwimeter ("/mm). So if de focaw wengf is measured in miwwimeters, de image scawe is

The derivation of dis eqwation is fairwy straightforward and de resuwt is de same for refwecting or refracting tewescopes. However, conceptuawwy it is easier to derive by considering a refwecting tewescope. If an extended object wif anguwar size α{\dispwaystywe \awpha } is observed drough a tewescope, den due to de Laws of refwection and Trigonometry de size of de image projected onto de focaw pwane wiww be

s=tan⁡(α)f.{\dispwaystywe s=\tan(\awpha )f.}

Thefore, de image scawe (anguwar size of object divided by size of projected image) wiww be

No tewescope can form a perfect image. Even if a refwecting tewescope couwd have a perfect mirror, or a refracting tewescope couwd have a perfect wens, de effects of aperture diffraction are unavoidabwe. In reawity, perfect mirrors and perfect wenses do not exist, so image aberrations in addition to aperture diffraction must be taken into account. Image aberrations can be broken down into two main cwasses, monochromatic, and powychromatic. In 1857, Phiwipp Ludwig von Seidew (1821–1896) decomposed de first order monochromatic aberrations into five constituent aberrations. They are now commonwy referred to as de five Seidew Aberrations.

The image of a point forms focaw wines at de sagittaw and tangentaw foci and in between (in de absence of coma) an ewwipticaw shape.

Curvature of Fiewd

The Petzvaw fiewd curvature means dat de image, instead of wying in a pwane, actuawwy wies on a curved surface, described as howwow or round. This causes probwems when a fwat imaging device is used e.g., a photographic pwate or CCD image sensor.

Distortion

Eider barrew or pincushion, a radiaw distortion dat must be corrected when combining muwtipwe images (simiwar to stitching muwtipwe photos into a panoramic photo).

Opticaw defects are awways wisted in de above order, since dis expresses deir interdependence as first order aberrations via moves of de exit/entrance pupiws. The first Seidew aberration, Sphericaw Aberration, is independent of de position of de exit pupiw (as it is de same for axiaw and extra-axiaw penciws). The second, coma, changes as a function of pupiw distance and sphericaw aberration, hence de weww-known resuwt dat it is impossibwe to correct de coma in a wens free of sphericaw aberration by simpwy moving de pupiw. Simiwar dependencies affect de remaining aberrations in de wist.

Two of de four Unit Tewescopes dat make up de ESO's VLT, on a remote mountaintop, 2600 metres above sea wevew in de Chiwean Atacama Desert.

Opticaw tewescopes have been used in astronomicaw research since de time of deir invention in de earwy 17f century. Many types have been constructed over de years depending on de opticaw technowogy, such as refracting and refwecting, de nature of de wight or object being imaged, and even where dey are pwaced, such as space tewescopes. Some are cwassified by de task dey perform such as Sowar tewescopes.

In a wens de entire vowume of materiaw has to be free of imperfection and inhomogeneities, whereas in a mirror, onwy one surface has to be perfectwy powished.

Light of different cowors travews drough a medium oder dan vacuum at different speeds. This causes chromatic aberration.

Refwectors work in a wider spectrum of wight since certain wavewengds are absorbed when passing drough gwass ewements wike dose found in a refractor or catadioptric.

There are technicaw difficuwties invowved in manufacturing and manipuwating warge-diameter wenses. One of dem is dat aww reaw materiaws sag in gravity. A wens can onwy be hewd by its perimeter. A mirror, on de oder hand, can be supported by de whowe side opposite to its refwecting face.

Comparison of nominaw sizes of primary mirrors of some notabwe opticaw tewescopes

Most warge research refwectors operate at different focaw pwanes, depending on de type and size of de instrument being used. These incwuding de prime focus of de main mirror, de cassegrain focus (wight bounced back down behind de primary mirror), and even externaw to de tewescope aww togeder (such as de Nasmyf and coudé focus).[23]

A new era of tewescope making was inaugurated by de Muwtipwe Mirror Tewescope (MMT), wif a mirror composed of six segments syndesizing a mirror of 4.5 meters diameter. This has now been repwaced by a singwe 6.5 m mirror. Its exampwe was fowwowed by de Keck tewescopes wif 10 m segmented mirrors.

The wargest current ground-based tewescopes have a primary mirror of between 6 and 11 meters in diameter. In dis generation of tewescopes, de mirror is usuawwy very din, and is kept in an optimaw shape by an array of actuators (see active optics). This technowogy has driven new designs for future tewescopes wif diameters of 30, 50 and even 100 meters.

Rewativewy cheap, mass-produced ~2 meter tewescopes have recentwy been devewoped and have made a significant impact on astronomy research. These awwow many astronomicaw targets to be monitored continuouswy, and for warge areas of sky to be surveyed. Many are robotic tewescopes, computer controwwed over de internet (see e.g. de Liverpoow Tewescope and de Fauwkes Tewescope Norf and Souf), awwowing automated fowwow-up of astronomicaw events.

Initiawwy de detector used in tewescopes was de human eye. Later, de sensitized photographic pwate took its pwace, and de spectrograph was introduced, awwowing de gadering of spectraw information, uh-hah-hah-hah. After de photographic pwate, successive generations of ewectronic detectors, such as de charge-coupwed device (CCDs), have been perfected, each wif more sensitivity and resowution, and often wif a wider wavewengf coverage.

Current research tewescopes have severaw instruments to choose from such as:

The phenomenon of opticaw diffraction sets a wimit to de resowution and image qwawity dat a tewescope can achieve, which is de effective area of de Airy disc, which wimits how cwose two such discs can be pwaced. This absowute wimit is cawwed de diffraction wimit (and may be approximated by de Rayweigh criterion, Dawes wimit or Sparrow's resowution wimit). This wimit depends on de wavewengf of de studied wight (so dat de wimit for red wight comes much earwier dan de wimit for bwue wight) and on de diameter of de tewescope mirror. This means dat a tewescope wif a certain mirror diameter can deoreticawwy resowve up to a certain wimit at a certain wavewengf. For conventionaw tewescopes on Earf, de diffraction wimit is not rewevant for tewescopes bigger dan about 10 cm. Instead, de seeing, or bwur caused by de atmosphere, sets de resowution wimit. But in space, or if adaptive optics are used, den reaching de diffraction wimit is sometimes possibwe. At dis point, if greater resowution is needed at dat wavewengf, a wider mirror has to be buiwt or aperture syndesis performed using an array of nearby tewescopes.

^gawiweo.rice.edu The Gawiweo Project > Science > The Tewescope by Aw Van Hewden "The Hague discussed de patent appwications first of Hans Lipperhey of Middewburg, and den of Jacob Metius of Awkmaar... anoder citizen of Middewburg, Sacharias Janssen had a tewescope at about de same time but was at de Frankfurt Fair where he tried to seww it"